On an Irreversible Investment Problem with Two-Factor Uncertainty

TL;DR

This paper models an irreversible investment problem with two independent stochastic product prices, characterizing the optimal investment boundary as a solution to a nonlinear integral equation and analyzing its sensitivity to parameters.

Contribution

It introduces a novel two-dimensional optimal stopping framework for a two-product investment problem with independent price uncertainties, providing analytical and numerical characterizations.

Findings

Optimal investment boundary is a convex curve solving a nonlinear integral equation.

The project value and investment decision are sensitive to model parameters.

Analytical and numerical comparative statics are provided.

Abstract

We consider a real options model for the optimal irreversible investment problem of a profit maximizing company. The company has the opportunity to invest into a production plant capable of producing two products, of which the prices follow two independent geometric Brownian motions. After paying a constant sunk investment cost, the company sells the products on the market and thus receives a continuous stochastic revenue-flow. This investment problem is set as a two-dimensional optimal stopping problem. We find that the optimal investment decision is triggered by a convex curve, which we characterize as the unique continuous solution to a nonlinear integral equation. Furthermore, we provide analytical and numerical comparative statics results of the dependency of the project's value and investment decision with respect to the model's parameters.